But I usually find a lot and pay the $40 or whatever it is

So you may as well just valet park at the hotel, or use the Copley Place or Prudential garages

Google maps are your friend. Plan on spending $20-30 for 1-2 hours.

I have had many appts in the area and have gotten lucky here more often than not, in finding a public metered space. As you come around on Dartmouth st by the Westin, head toward the entrance to mass pike, but go right, onto Blagden, which borders the library. Lots of metered spots there. It ends at Exeter, where you have to go left - also some spots there.  If you strike out, go straight into the Copley Mall garage. Spend a few bucks in the mall and get validated for a break on their rates.

One more thing: download the ParkBoston app on your phone and pay for meters that way. Great app, you can always check it to see how much time you have left, add time, etc.